More Like this

1. Multiple testing approaches for hypotheses in integrative genomics

   https://doi.org/10.1002/wics.1493  

   Rudra, Pratyaydipta ; Cruz‐Cortés, Efrén ; Zhang, Xuhong ; Ghosh, Debashis ( December 2019 , WIREs Computational Statistics)

   With the explosion in available technologies for measuring many biological phenomena on a large scale, there have been concerted efforts in a variety of biological and medical settings to perform systems biology analyses. A crucial question then becomes how to combine data across the various large‐scale data types. This article reviews the data types that can be considered and treats so‐called horizontal and vertical integration analyses. This article focuses on the use of multiple testing approaches in order to perform integrative analyses. Two questions help to clarify the class of procedures that should be used. The first deals with whether a horizontal or vertical integration is being performed. The second is if there is a priority for a given platform. Based on the answers to these questions, we review various methodologies that could be applied.

   This article is categorized under:

   Statistical Learning and Exploratory Methods of the Data Sciences > Knowledge Discovery

   Statistical and Graphical Methods of Data Analysis > Nonparametric Methods

   Applications of Computational Statistics > Genomics/Proteomics/Genetics

    

   more » « less
2. A Two-Sample Distribution-Free Test for Functional Data with Application to a Diffusion Tensor Imaging Study of Multiple Sclerosis

   https://doi.org/10.1111/rssc.12130  

   Pomann, Gina-Maria ; Staicu, Ana-Maria ; Ghosh, Sujit ( January 2016 , Journal of the Royal Statistical Society Series C: Applied Statistics)

   Motivated by an imaging study, the paper develops a non-parametric testing procedure for testing the null hypothesis that two samples of curves observed at discrete grids and with noise have the same underlying distribution. The objective is to compare formally white matter tract profiles between healthy individuals and multiple-sclerosis patients, as assessed by conventional diffusion tensor imaging measures. We propose to decompose the curves by using functional principal component analysis of a mixture process, which we refer to as marginal functional principal component analysis. This approach reduces the dimension of the testing problem in a way that enables the use of traditional non-parametric univariate testing procedures. The procedure is computationally efficient and accommodates different sampling designs. Numerical studies are presented to validate the size and power properties of the test in many realistic scenarios. In these cases, the test proposed has been found to be more powerful than its primary competitor. Application to the diffusion tensor imaging data reveals that all the tracts studied are associated with multiple sclerosis and the choice of the diffusion tensor image measurement is important when assessing axonal disruption.

    

   more » « less
3. Variational Approximation based Model Selection for Microbial Network Inference

   Yooseph, Shibu ; Tavakoli, Sahar ( January 2022 , Journal of computational biology)

   Singh, Mona (Ed.)

   Microbial associations are characterized by both direct and indirect interactions between the constituent taxa in a microbial community, and play an important role in determining the structure, organization, and function of the community. Microbial associations can be represented using a weighted graph (microbial network) whose nodes represent taxa and edges represent pairwise associations. A microbial network is typically inferred from a sample-taxa matrix that is obtained by sequencing multiple biological samples and identifying the taxa counts in each sample. However, it is known that microbial associations are impacted by environmental and/or host factors. Thus, a sample-taxa matrix generated in a microbiome study involving a wide range of values for the environmental and/or clinical metadata variables may in fact be associated with more than one microbial network. Here we consider the problem of inferring multiple microbial networks from a given sample-taxa count matrix. Each sample is a count vector assumed to be generated by a mixture model consisting of component distributions that are Multivariate Poisson Log-Normal. We present a variational Expectation Maximization algorithm for the model selection problem to infer the correct number of components of this mixture model. Our approach involves reframing the mixture model as a latent variable model, treating only the mixing coefficients as parameters, and subsequently approximating the marginal likelihood using an evidence lower bound framework. Our algorithm is evaluated on a large simulated dataset generated using a collection of different graph structures (band, hub, cluster, random, and scale-free). 

   more » « less
4. Structural Re-weighting Improves Graph Domain Adaptation

   Shikun Liu, Tianchun Li ( July 2023 , International Conference on Machine Learning Big Data and Business Intelligence)

   In many real-world applications, graph-structured data used for training and testing have differences in distribution, such as in high energy physics (HEP) where simulation data used for training may not match real experiments. Graph domain adaptation (GDA) is a method used to address these differences. However, current GDA primarily works by aligning the distributions of node representations output by a single graph neural network encoder shared across the training and testing domains, which may often yield sub-optimal solutions. This work examines different impacts of distribution shifts caused by either graph structure or node attributes and identifies a new type of shift, named conditional structure shift (CSS), which current GDA approaches are provably sub-optimal to deal with. A novel approach, called structural reweighting (StruRW), is proposed to address this issue and is tested on synthetic graphs, four benchmark datasets, and a new application in HEP. StruRW has shown significant performance improvement over the baselines in the settings with large graph structure shifts, and reasonable performance improvement when node attribute shift dominates. 

   more » « less
5. Scalable and Efficient Hypothesis Testing with Random Forests

   Coleman, Tim ; Peng, Wei ; Mentch, Lucas ( June 2022 , Journal of machine learning research)

   Allen, Genevra (Ed.)

   Throughout the last decade, random forests have established themselves as among the most accurate and popular supervised learning methods. While their black-box nature has made their mathematical analysis difficult, recent work has established important statistical properties like consistency and asymptotic normality by considering subsampling in lieu of bootstrapping. Though such results open the door to traditional inference procedures, all formal methods suggested thus far place severe restrictions on the testing framework and their computational overhead often precludes their practical scientific use. Here we propose a hypothesis test to formally assess feature significance, which uses permutation tests to circumvent computationally infeasible estimates of nuisance parameters. This test is intended to be analogous to the F-test for linear regression. We establish asymptotic validity of the test via exchangeability arguments and show that the test maintains high power with orders of magnitude fewer computations. Importantly, the procedure scales easily to big data settings where large training and testing sets may be employed, conducting statistically valid inference without the need to construct additional models. Simulations and applications to ecological data, where random forests have recently shown promise, are provided. 

   more » « less